Quantum low-density parity-check (QLDPC) codes with good parameters are promising candidates for low-overhead fault-tolerant quantum computing, but their non-local stabilizers require long-range connectivity and frequent qubit movement, introducing practical challenges. Prior work has studied the networked implementation of topological codes, where each node only holds one or a few qubits of the entire code, and demonstrated competitive performance under practical constraints such as the quality of network-provided entanglement. However, since these codes are already geometrically local, such a networked setting might not be essential. In this work, we propose and study the networked implementation of better QLDPC codes, specifically bivariate bicycle codes due to their similarity to surface codes and the controlled amount of long-range connections in their stabilizers. We begin by recreating networked surface codes in Stim, with one code qubit per node, and provide additional insights into their circuit-level noise performance. We then extend this approach to bipartitions of bivariate bicycle codes, using balanced min-cut partitioning on their combined X-Z Tanner graph to identify optimal qubit splits. For stabilizers spanning nodes, we implement teleported CNOTs and vary the Bell pair fidelity enabling these gates. Through circuit-level noise simulations with BP-OSD decoding, we provide the first insights into networked realizations of these codes and compare their performance with monolithic implementations. We conclude by outlining advantages, limitations, and future directions.

翻译：具有优良参数的量子低密度奇偶校验码（QLDPC codes）是实现低开销容错量子计算的重要候选方案，但其所依赖的非局域稳定子需要长程连接和频繁的量子比特移动，这带来了实际应用中的挑战。先前研究已经探讨了拓扑码的网络化实现方案——在该方案中，每个节点仅持有整个码字的一个或少数几个量子比特，并在网络提供纠缠质量等实际约束条件下展现出优异的性能表现。然而，由于这些拓扑码本身已具有几何局域性，网络化设置并非必要。本研究提出并深入探讨了性能更优的QLDPC码的网络化实现，特别关注双变量循环码——此类码因与表面码具有相似性，且其稳定子包含可控数量的长程连接。我们首先在Stim仿真器中重建了每个节点含一个码字量子比特的网络化表面码，并提供了关于其电路级噪声性能的新见解。随后将该方法扩展至双变量循环码的二部划分，通过对其组合X-Z Tanner图进行平衡最小割划分来确定最优量子比特拆分方案。对于跨越节点的稳定子，我们实现远程受控非门操作，并改变用于实现这些门的贝尔态保真度参数。通过结合BP-OSD解码的电路级噪声仿真，首次揭示了此类码的网络化实现特性，并与单片实现方案进行了性能对比。最后，我们总结了本方案的优势、局限性及未来研究方向。